It is easy to verify that (REF ) can be slightly weakened by replacing `everywhere on \(\mathbb {R}^n\) ' by `nearly everywhere on \(\mathbb {R}^n\) ' (see e.g. the author's recent result [1]}, establishing the principle of positivity of mass for potentials with respect to rather general function kernels on locally compact spaces). Recall that a proposition involving a variable point \(x\in \mathbb {R}^n\)  is said to hold nearly everywhere (n.e.) on \(A\subset \mathbb {R}^n\)  if \(c_\alpha (E)=0\) , where \(E\)  is the set of \(x\in A\)  for which the proposition fails to hold, while \(c_\alpha (E)\)  is the inner \(\alpha \) -Riesz capacity of \(E\)  [2]} (cf. Sect.  below).
